Horizontal and vertical variability of observed soil temperatures

Two datasets of soil temperature observations collected at Norman, Oklahoma, USA, were analysed to study horizontal and vertical variability in their observations. The first dataset comprised 15‐min resolution soil temperature observations from 20 September 2011 to 18 November 2013 in seven plots across a 10‐m transect. In each plot, sensors were located at depths of 5, 10, and 30 cm. All seven plots observed fairly consistent maximum soil temperature observations during the spring, fall, and winter months. Starting in late May, the observed spread in soil temperatures across the 10‐m transect increased significantly until August when the observed spread in temperatures decreased. The range of observed minimum soil temperature was more consistent year‐round at the shallower depths, but showed similar patterns to the maximum soil temperature ranges at deeper depths. The second dataset comprised 15‐min resolution soil temperature observations from 20 November 2013 to 1 December 2015 in a single plot at the same location as the first dataset. Soil temperature sensors were placed every 2 cm from the surface down to 40 cm deep to study the vertical variability in soil temperature measurements (focusing on a winter and a summer case). Both winter and summer conditions showed that the temperature differences between depths behaved logarithmically with the shallower depths having larger differences than deeper depths.


Introduction
Soil temperature measurements are important to many end users ranging from those in the agricultural sector (Stone et al., 1999;Mavi and Tupper, 2004;Patil et al., 2010) to meteorological modellers (Godfrey and Stensrud, 2008) to engineering (Omer, 2008). As a result, more observations of soil temperatures are being collected in networks of varying spatial scales from single watersheds (Cosh et al., 2008;Steiner et al., 2008) to regional (McPherson et al., 2007) to national in scope (Schaefer et al., 2007). With any type of observing methodology, challenges exist in ensuring high-quality data are collected and in understanding the limitations of those observations. In addition, the variability in those observations must be understood to best utilize the collected data. Soil temperature observations are impacted by many factors that can cause variabilities in their measurements (Davidoff and Selim, 1988;Shumway et al., 1989;Mohanty et al., 1995).
Understanding the range of temperatures inherent across an observing station allows one to more accurately quality assure the data. In addition, due to the erosion or deposition of soil, understanding vertical variability in soil temperatures can provide knowledge of the impacts from small depth changes to measured values. Scharringa (1976) showed that horizontal and vertical gradients can become quite large in the nearsurface profile of the soil. Their work showed that variances can reach 1.2°C at 5 cm, 0.9°C at 10 cm, and 0.8°C at 20 cm over a 20 m 9 21 m plot of bare sandy soil. In addition, variations in soil temperatures can exist due to vegetation (Scharringa, 1976) or altering of the soil surface from heavy rains or cracks due to drought (Fiebrich and Crawford, 2001;Fiebrich et al., 2010).
The Oklahoma Mesonet (doi: 10.15763/ dbs.mesonet), commissioned in 1994, is an automated network of 121 remote, meteorological stations across Oklahoma (Brock et al., 1995;McPherson et al., 2007). Each station measures core parameters that include: air temperature and relative humidity at 1.5 m; wind speed, gust, and direction at 10 m; wind speed at 2 m; atmospheric pressure; global downwelling solar radiation; rainfall; bare soil temperature at 10 cm below ground level; and vegetated soil temperatures at 5 and 10 cm below ground level. In addition, many stations also measured or currently measure bare soil temperature at 5 cm; vegetated soil temperature at 25 or 30 cm; and soil moisture at 5, 25, and 60 cm. Mesonet data are collected and transmitted to a central facility every 5 min where they are quality controlled, distributed, and archived (Shafer et al., 2000;http://mesonet.org). The Oklahoma Mesonet has measured soil temperature under bare soil and native vegetation since 1994 at over 100 sites.

Materials and methods
To better understand the spatial variability in soil temperature, two separate experiments were conducted by the Oklahoma Mesonet: a comparison between seven plots of soil temperature probes across a 10-m transect (e.g. the width of a Mesonet station) and an analysis of 21 soil temperature probes placed 2 cm apart vertically in a single location. Data were collected for over 4 years to provide a sufficient number of observations for analysis.
The soil temperature sensors utilized in these studies were BetaTHERM stainless steel encased 10 K thermistor assemblies (Part # 10K3D410 made by Measurement Specialties in Shrewsbury, MA). The Oklahoma Mesonet used this style of sensor operationally between 1996and 2013(McPherson et al., 2007. The BetaTHERM assemblies are a 10K NTC thermistor housed in a 0.32-cm-diameter, 15-cm-long stainless steel sheath with the thermistor bead potted inside the end of the sheath. These sensors have a calibrated range of À20°C to 60°C with an accuracy of AE0.5°C. Each sensor went through quality control in the Oklahoma Mesonet's calibration laboratory before deployment (McPherson et al., 2007). Upon completion of the study, each sensor was reanalysed in the Mesonet's calibration laboratory to ensure that no bias or drift had occurred during field use.

Horizontal variability study
In order to study the horizontal variability in soil temperatures, seven identical installations of soil temperature sensors were placed across a 10-m transect near the Norman, Oklahoma Mesonet station ( Figure 1). Each plot utilized a PVC track with holes at the appropriate measurement depths to reduce soil upheaval and ensure that the sensors remained at the required depths. Each plot had soil temperature sensors inserted horizontally through the PVC track at depths of 5, 10, and 30 cm. These depths were selected to match existing soil temperature measurements depths of the Oklahoma Mesonet. The sensors' wires were looped downwards before emerging from the plot to eliminate preferential flow of rainfall down the wire and to the sensor. Each sensor was wired into a datalogger for data collection every 15 min. Data were collected for over 2 years from 20 September 2011 to 18 November 2013 and were manually quality assured by an Oklahoma Mesonet research scientist. The vegetation at the study site was controlled regularly to maintain similar conditions to the surrounding native vegetation. The soil textures at the study location were silty clay (i.e. 8.3% sand, 49.0% silt, and 42.7% clay) at 5 cm, silty clay loam (i.e. 17.7% sand, 48.4% silt, and 33.9% clay) at 25 cm, and silty clay (i.e. 12.5% sand, 41.5% silt, and 46.0% clay) at 60 cm.

Vertical variability study
Upon conclusion of the horizontal variability study at the Norman, Oklahoma Mesonet station, the study area was reconfigured to analyse the vertical variability in soil temperature measurements. All 21 sensors were moved to one plot and placed every 2 cm from the surface (the first sensor positioned at ground level) down to 40 cm ( Figure 2). Similar to the previous study, the sensors were mounted through a PVC track to ensure that each sensor remained at its desired depth with its wires looped downwards to reduce the impact of preferential flow of rain water. Data were collected every 15 min for over 2 years from 20 November 2013 to 1 December 2015 and were manually quality assured.

Horizontal variability study
It became immediately obvious that even though each of the seven test plots were installed with calibrated sensors at identical depths, they rarely recorded identical soil temperatures. The range of temperatures observed across the seven plots varied by depth of the sensor, by time of the year, and by time of day. The predominate impact to the variability in soil temperature measurements came from summer-time heat, but rainfall events also contributed to changes in soil temperature variability during the spring months.
The range of maximum daily soil temperatures at a depth of 5 cm can be seen in Figure 3(a). The range of maximum temperatures across the seven plots was between 1.0 and 2.0°C for most of the year. However, once daily maximum soil temperatures at 5 cm reached~30°C, the range of maximum daily temperatures varied by~4.5°C in 2012 and~6.0°C in 2013. Thus, it would be impossible to accurately characterize the maximum soil temperature at 5 cm during the summer months with a single sensor. The range of minimum daily temperatures of soil temperatures observed at a depth of 5 cm is shown in Figure 3(b). The minimum temperatures across the seven plots varied between 0.5 and 1.5°C for most of the year.
The range of observed maximum daily soil temperatures across the seven plots at a depth of 10 cm is shown in Figure 3(c). The range of temperatures had a very similar pattern to the 5 cm data. Maximum daily temperatures at 10 cm varied by 0.5-1.5°C for most of the year. Again, once daily maximum soil temperatures at 10 cm reached~30°C, the range of observed temperatures increases to~3.0°C in 2012 and~4.5°C in 2013 across the plots. During the spring months, the ranges oscillated up and down due to synoptic scale rainfall and heating/cooling patterns. The range of minimum daily soil temperatures at 10 cm is shown in Figure 3(d). The range of temperatures across the seven plots was~0.5°C for most of the year.
The range of maximum daily soil temperatures at 30 cm can be seen in Figure 3(e). The range of temperatures across the seven plots had a very similar pattern to the 5 and 10 cm data with ranges slightly less at~0.5°C across the seven plots for most of the year. Once daily maximum soil temperatures at 30 cm reached~25°C, the range of temperature values increased to~2.0°C in 2012 and~1.5°C in 2013. The range of minimum daily soil temperatures at 30 cm is shown in Figure 3(f). Minimum temperatures across the seven plots generally agreed within 0.5°C for most of the year with an increase in variability during the summer warming periods.
Overall, all three soil temperature depths showed similar patterns with smaller variability at deeper depths throughout the year. At 5, 10, and 30 cm, the horizontal range of soil temperatures remained consistent during the spring, fall, and winter months with the range of maximum temperatures at 0.3-2.0°C, 0.3-1.5°C, and 0.3-0.5°C, respectively, and the range of minimum temperatures at 0.3-1.3°C, 0.3-1.0°C, and 0.2-0.5°C. During the late spring, the ranges of soil temperatures peaked in August at values of 4.5-6.5°C, 3.0-4.5°C, and 1.5-2.0°C for maximum temperatures and 1.5-2.5°C, 1.5-2.0°C, and 1.5-2.0°C for minimum temperatures. The ranges then quickly decreased during the cooler seasons. The difference in larger variabilities in maximum soil temperatures between the summers of 2012 and 2013 is likely due to different soil moisture conditions (not shown). The soil remained dry throughout the soil column during summer of 2012, while the soil was more consistently wet at deeper depths during the summer of 2013. This likely led to the reduced variability at 30 cm during the summer of 2012.

Vertical variability study
To understand the variability in soil temperatures with depth, the diurnal range of temperatures at different depths must be considered as soil temperatures at 2 cm observe larger diurnal ranges than those at 40 cm. In addition, the air temperature, the thermal load, and soil moisture conditions all impact heat transfer rates through the soil profile. Due to different temperature change rates depending upon depth, analysis of the vertical stratification of soil temperatures was performed at the temperatures' maximum or minimum values. Typically, at sunset during the winter and just after sunrise in the summer, all of the temperatures were nearly identical. In addition, rainfall events and frontal passages caused inconsistencies in the typical vertical stratifications of soil temperatures. As a result, 2 weeks (one summer and one winter) with calm, synoptic conditions were analysed to most accurately determine how soil temperatures were vertically stratified.
Vertical soil temperature data from a winter week (15 January 2014-21 January 2014) are shown in Figure 4(a). For each day (e.g. Figure 4(c)), the transfer of heat through the soil profile caused all depths to observe relatively homogeneous soil temperatures near sunset (~01 UTC). Daily minimum temperatures typically occurred shortly after sunrise with the coldest temperatures at the surface and warmest temperatures at deeper depths. The change in soil temperature with depth decreased logarithmically with depth as shown from the 19 January data (Figure 4(e); Table 1). A linear regression was performed and a  (Figure 4(d)), the shallower depths peaked earliest (e.g. 2045 UTC at 2 cm) while the deeper depths peaked over the next few hours (e.g. 0215 UTC at 20 cm; 0615 UTC at 30 cm; and 0845 UTC at 40 cm). Similar to the winter week, the differences between the maximum temperature of the day for the sensor at the depth above it changed at a logarithmic rate as shown from the 22 August 2014 data (Figure 4(f); Table 1). A linear regression was performed and a resulting logarithmic equation was derived (Figure 4(f)) that gave a mean square error of 0.9780; however, this equation is likely only applicable in soil profile characteristics similar to this study site. Similar logarithmic patterns were observed each day with only slight variations.
Overall, vertical variability in soil temperatures is difficult to quantify due to many external sources that can impact sensors at different times and at different rates. However, both winter and summer conditions showed that the temperature differences between depths changed logarithmically with the shallower depths having larger differences than deeper depths. The winter week had smaller changes than the summer, but this is to be expected given that the diurnal temperature during that period was much smaller allowing for fewer heat loads and releases.

Conclusions
The goal of these analyses was to better understand the horizontal and vertical variability in soil temperature measurements. Looking horizontally across a 10-m transect, observations of maximum soil temperature typically varied between 0.3 and 2.0°C from early fall through late spring. Over the summer, the variability in maximum soil temperature increased to over 6.5°C over seven closely located plots. For minimum soil temperatures, soil temperatures across a 10-m transect typically varied between 0.3 and 1.3°C from early fall through late spring, but increased to over 2.5°C in the summer. When looking at a vertical profile of soil temperatures, the temperature differences between depths varied logarithmically with the shallower depths having larger differences (over 0.67°C/cm in the summer and over 0.33°C/cm in the winter at 10 cm or shallower) than deeper depths (over 0.11°C/cm in the summer and over 0.10°C/cm in the winter at 10 cm or deeper) and colder season temperatures having smaller changes than those during the warm season. With the knowledge gained from this study, those making decisions using soil temperature observations can have a better understanding of its horizontal and vertical variability.